In the above-identified commonly owned applications there has been disclosed an automatic speed-changing system of this type wherein two clutches and a brake are accommodated in a common transmission housing, the first clutch including a clutch housing positively connected with an extremity of an input shaft whereas the second clutch comprises a clutch housing positively connected with an extremity of the outer one of the two nested output shafts. The two clutches further include respective sets of annular friction foils both carried on an extension of the first clutch housing; as shown but not claimed in these earlier applications, that extension has the shape of a generally cylindrical sleeve whose inner peripheral surface is formed with ribs for the guidance of alternate friction foils of the first clutch while its outer peripheral surface has ribs guiding alternate foils of the second clutch. These sleeve-supported foils respectively coact with interleaved foils guided on a collar splined to a projecting extremity of the inner output shaft in the case of the first clutch and on the second clutch housing in the case of the second clutch.